In the opening scenes of Almost Human, future cop Kennex (Karl Urban) has a limb blown off during a botched raid. UK channel Watch, which launched the JJ Abrams-produced sci-fi drama on Tuesday night, might also feel slightly under fire. Last week, it was confirmed that Almost Human wouldn't be picked up for a second season. Suddenly, Watch's "hit US show" – as it was described in splashy print and online banner ads – seemed more like a lame duck, a one-season blunder.

It's a shame because Almost Human is better than most of the cop shows currently on TV. In its flat, bright, tech-heavy vision of 2048, every human detective is paired with a ruthlessly logical MX android: part-PDA, part-Terminator. Kennex, now with a synthetic leg, is partnered with Dorian (played with wry serenity by Michael Ealy), an older model mothballed for mysterious reasons.

Mismatched cops have edged towards mutual respect a million times on screen, and the trope of a Pinocchio robot trying to work out what it is to be human feels almost as cliched. But Almost Human's twist is that Dorian demonstrates more emotional intelligence than the volatile Kennex, who aggressively alienates himself from both humans and androids. The scenes where they roll around in their police cruiser needling each other are so absorbing and entertaining – a wifi-enabled bromance – that the additional solving of future crime begins to feel more like an imposition than an imperative.

If the show had made it beyond these first 13 episodes, it's unlikely that Almost Human would ever have wriggled completely out of its procedural framework, although there's an anarchic, almost slapstick undercurrent to its otherwise ergonomic, po-faced future. But television doesn't need to be long-lived to be worth watching. As viewers, we're conditioned to equate Almost Human with failure, even though that metric is economic rather than aesthetic. Networks are as rigid and unswerving as MX androids, crunching numbers to decide what shows deserve to continue.

Certain TV shows carry their early cancellation as a badge of honour: there's an agreed canon of one-season wonders that includes Freaks And Geeks, Firefly, Police Squad and My So-Called Life. But I also carry a torch for other shows that failed to complete more than one lap on the small screen, a handful of slim novellas to stack up alongside the Tolstoy girth of The Wire, The Sopranos and those other big beasts of heavily serialised storytelling.

Some feel like early, rough-and-ready EPs by your favourite band. Karen Sisco – the short-lived, hard-to-find Out Of Sight spin-off starring Carla Gugino as a US Deputy Marshal in Miami – is so packed with the distinctive flavour of Elmore Leonard that it feels like a sunny warm-up for Justified. Wonderfalls, the whimsical, moving 13-episode story of a gift-shop clerk who appears to receive messages from God through various knick-knacks is a decade old, but planted a collaborative seed: creator Bryan Fuller and star Caroline Dhavernas recently reunited for Hannibal.

Colin Hanks is very good in Fargo, but he was great a couple of years ago in The Good Guys, starring opposite Bradley Whitford's astonishing moustache. At first glance, the show looked like an homage to 1980s action-adventure junk such as Simon And Simon, but the breezy familiarity was counterbalanced by radical experiments in narrative storytelling, whizzing back and forth through each episode's timeframe.

Approaching the end of The Good Guys, I slowed down, soaking up each episode in the knowledge that there was a finite number of episodes. I did the same with The Beast. Patrick Swayze was diagnosed with pancreatic cancer at the outset of filming, and even though the milieu of undercover FBI agents losing their moral compass felt well-worn, his performance – burdened, intense, angry – gave The Beast resonance.

These shows, and others like them, deserve to be more than footnotes: scenic routes that are also shortcuts, where unresolved endings help keep characters and worlds alive, preserved in the aspic of a single DVD box. Best of all, shows that only lasted one season rarely betray your investment in them. (I'm looking at you, Dexter.)

So do you have a favourite overlooked show that only lasted one season? Let us know.